Information processing apparatus, ising device, and method for controlling information processing apparatus

ABSTRACT

In an information processing apparatus, a calculation circuit calculates energy values representing total energies of Ising devices that are set up with different noise widths, where the Ising devices have equal conditions about neuron-to-neuron connections. An exchange control circuit exchanges output values of neurons or noise widths, between first and second Ising devices having adjacent noise widths. This exchange takes place with an exchange probability based on a difference in the energy values between the first Ising device and the second Ising device.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2016-131285, filed on Jul. 1, 2016, the entire contents of which are incorporated herein by reference.

FIELD

The embodiments discussed herein relate to an information processing apparatus, an Ising device, and a method for controlling an information processing apparatus.

BACKGROUND

Ising devices, or Boltzmann machines, are known as a technique for solving multivariable optimization problems, for which the von Neumann computer architecture does not always work well. Ising devices execute a process called “simulated annealing” using energy functions of the Ising model that represents behavior of atomic spins in magnetic substances. That is, Ising devices solve a given problem by transforming it to an Ising model problem.

As an example of techniques related to Ising devices, one proposed parallel processing method uses multiple Ising devices implemented in hardware. Another proposed technique is to compare evaluation scores of Ising devices, update inferior evaluation scores, and when identical scores are found, output them as an optimal solution. See, for example, the following documents:

Japanese Laid-open Patent Publication No. 5-250346

Japanese Laid-open Patent Publication No. 8-272760

C. R. Schneider and H. C. Card, “Analog CMOS Deterministic Boltzmann Circuits”, Journal of Solid-State Circuits, pp. 907-914, 1993

A. DeGloria et al., “Efficient Implementation of the Boltzmann Machine Algorithm”, IEEE Trans of NN, pp. 159-163, 1993

A. DeGloria et al., “Design and Performance Evaluation of a Parallel Architecture for the Boltzmann Machine”, EuroMICRO, pp. 629-636, 1994

As mentioned above, hardware-based implementation of Ising devices is possible. However, even with such Ising devices, the computational process takes a long time to reach an optimal solution because it includes sequential operations that have to be repeated many times.

SUMMARY

In one aspect, there is provided an information processing apparatus including: a plurality of Ising devices each including a neuron circuit block that calculates as many first energy values as a number of neurons, based on weight values representing strengths of neuron-to-neuron connections and output values of the neurons, and determines and outputs new output values, based on comparison results between a threshold and each of the first energy values plus a noise value, the plurality of Ising devices having equal conditions about neuron-to-neuron connections represented by the weight values, the plurality of Ising devices being set up with different noise widths each representing a difference between a lower limit and an upper limit of noise values; a calculation circuit that calculates second energy values respectively representing total energies of the plurality of Ising devices, based on the first energy values and the output values; an exchange control circuit that exchanges output values or noise widths between a first Ising device and a second Ising device among the plurality of Ising devices, with an exchange probability based on a difference in the second energy values between the first Ising device and the second Ising device, the first and second Ising devices respectively having first and second noise widths, the second noise width being adjacent to the first noise width; and a controller device that sets the different noise widths to the plurality of Ising devices.

The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates an example of an information processing apparatus according to a first embodiment;

FIG. 2 illustrates how a plurality of ensembles with different temperatures exchange their node states;

FIG. 3 illustrates energy functions of ensembles with different temperatures;

FIG. 4 illustrates an example of an information processing apparatus according to a second embodiment;

FIG. 5 illustrates an exemplary distribution of probability P_(i) (h_(i)) of output value x_(i)=1;

FIG. 6 illustrates an example of a calculation circuit;

FIG. 7 illustrates an example of an exchange control circuit;

FIG. 8 illustrates an example of a flag generator circuit;

FIG. 9 illustrates another example of a flag generator circuit;

FIG. 10 illustrates an example of an exchange circuit;

FIG. 11 illustrates a truth table that indicates an exemplary relationship between input signals and output signals of a selection signal generator circuit;

FIG. 12 illustrates a truth table that indicates an exemplary relationship between input signals and output signals of a state selection circuit;

FIGS. 13 and 14 are the first and second parts of a flowchart illustrating exemplary operation of an information processing apparatus according to the second embodiment;

FIG. 15 illustrates an example of an information processing apparatus according to a third embodiment;

FIG. 16 illustrates an example of an exchange control circuit;

FIG. 17 illustrates an example of a temperature setting signal generator circuit;

FIG. 18 illustrates a truth table that indicates an exemplary relationship between input signals and output signals of a temperature setting signal generator circuit;

FIG. 19 is a flowchart illustrating exemplary operation of the information processing apparatus according to the third embodiment; and

FIG. 20 is a timing diagram illustrating exemplary operation of the information processing apparatus.

DESCRIPTION OF EMBODIMENTS

Several embodiments will be described in detail below with reference to the accompanying drawings.

(a) First Embodiment

FIG. 1 illustrates an example of an information processing apparatus according to a first embodiment. This information processing apparatus 1 includes Ising devices 2 a 1 to 2 aN, a calculation circuit 3, an exchange control circuit 4, and a controller device 5. An optimization problem using energy functions is mapped onto Ising devices 2 a 1 to 2 aN, under the control of a controller device 5. Each Ising device 2 a 1 to 2 aN is implemented in the form of a single semiconductor integrated circuit (chip). These Ising devices 2 a 1 to 2 aN are similar to each other in terms of their components. For example, the illustrated Ising device 2 ak has a neuron circuit block 10 ak, and a control circuit 10 bk.

The neuron circuit block 10 ak calculates as many energy values as the number of neurons, based on weight values representing the strengths of neuron-to-neuron connections, as well as on output values of the neurons. The energy values are referred to as “local field values” in the following description.

The weight values are specified by, for example, the controller device 5, depending on what optimization problem is being handled. That is, the controller device 5 writes specific weight values into Ising devices 2 a 1 to 2 aN, thereby mapping an optimization problem onto the Ising devices 2 a 1 to 2 aN.

The neuron circuit block 10 ak adds some noise values to local field values and compares the respective sums with a threshold. Based on the result of this comparison, the neuron circuit block 10 ak determines and outputs the output values mentioned above. The following description uses an integer n to indicate the number of neurons.

Referring to the example of FIG. 1, the neuron circuit block 10 ak includes n neuron circuits 11 k 1, 11 k 2, . . . , and 11 kn to implement the functions of n neurons. Each neuron circuit 11 k 1 to 11 kn executes the above-noted process of calculating a local field value and determining and outputting a one-bit output value of the corresponding neuron. When there is a change in one of the n output values (or n-bit output value) from the neurons, an update signal is generated. Each neuron circuit 11 k 1 to 11 kn has a function of updating its own local field value upon receipt of such an update signal.

The control circuit 10 bk supplies the neuron circuits 11 k 1 to 11 kn with the update signals noted above. For example, one update signal includes a changed output value and a selection signal for weight values. This selection signal specifies which weight to choose, depending on the identifier of the neuron circuit that has changed its output value.

For example, the above-described control circuit 10 bk may be implemented as a collection of comparator circuits, selector circuits, and other circuits. The control circuit 10 bk may be implemented by using one or more processors. For example, the processors include a central processing unit (CPU), micro processing unit (MPU), digital signal processor (DSP), application-specific integrated circuit (ASIC), programmable logic device (PLD), or any combination of these devices.

The Ising devices 2 a 1 to 2 aN are configured with the above-described elements, and their respective sets of neurons are connected in the same way (i.e., they have the same set of weight values). In other words, the neuron circuit blocks 10 a 1, 10 a 2, . . . , 10 ak, . . . , and 10 aN included in the Ising devices 2 a 1 to 2 aN have a plurality of neuron circuits with the same weighted connections. Because of these same weighted neural connections, the Ising devices 2 a 1 to 2 aN respectively calculate identical optimization problems in an independent manner. These Ising devices 2 a 1 to 2 aN are, however, set up with different noise widths. The term “noise width” refers to the extent (distance) between upper and lower limits of noise values used in the Ising devices 2 a 1 to 2 aN. In other words, the noise values used in each Ising device may vary within a different range.

Based on the local field values and n-bit output values of energy of the individual Ising devices 2 a 1 to 2 aN, the calculation circuit 3 calculates energy values (E1, E2, . . . , Ek, . . . , EN) each representing the total amount of energy in the individual Ising devices 2 a 1 to 2 aN. For example, the calculation circuit 3 multiplies the local field value of the first neuron circuit 11 k 1 by the output value of the same. The calculation circuit 3 also performs a similar multiplication for each of the other neuron circuits 11 k 2 to 11 kn. The calculation circuit 3 then adds up the resulting products to yield an energy value Ek of the k-th Ising device 2 ak. In other words, the calculation circuit 3 obtains an energy value Ek by performing multiply-accumulate (MAC) operations on the local field values and output values that the neuron circuits 11 k 1 to 11 kn provide.

The exchange control circuit 4 controls exchange of n-bit output values or noise widths between two of the Ising devices 2 a 1 to 2 aN, where the two Ising devices are set up with noise widths that are adjacent to each other. The exchange takes place with a probability based on a difference in the above-described energy values between the two Ising devices. Such exchanges are part of an extended ensemble method (described later), and the probability of their occurrence is called “exchange probability.”

Noise width is equivalent to effective temperature T in equation (5) described later. Expanding a noise width means raising effective temperature T. The Ising devices 2 a 1 to 2 aN in FIG. 1 are respectively given different effective temperatures T₁, T₂, . . . , T_(k), . . . , and T_(N). The first Ising device 2 a 1 has a first noise width corresponding to effective temperature T₁, and the second Ising device 2 a 2 has a second noise width corresponding to effective temperature T₂. In the case of T₁>T₂> . . . >T_(k)> . . . >T_(N), the first and second Ising devices 2 a 1 and 2 a 2 are “adjacent” in terms of their noise widths. The exchange control circuit 4 thus exchanges their n-bit output values (or their noise widths) with each other, with an exchange probability based on the difference between energy values E1 and E2 of the two Ising devices 2 a 1 and 2 a 2.

The calculation circuit 3 and exchange control circuit 4 may be provided outside the Ising devices 2 a 1 to 2 aN as in the example of FIG. 1. Alternatively, either or both of the calculation circuit 3 and exchange control circuit 4 may be incorporated into the Ising devices 2 a 1 to 2 aN.

The controller device 5 configures each Ising device 2 a 1 to 2 aN with a uniquely different noise width. For example, the controller device 5 gives different noise widths to the Ising devices 2 a 1 to 2 aN upon receipt of a startup signal from an external source, such that their effective temperatures T will be T₁>T₂> . . . >T_(k)> . . . >T_(N).

The controller device 5 outputs an end signal to indicate completion of the current computation when a neuron settlement signal arrives from one of the Ising devices 2 a 1 to 2 aN. This neuron settlement signal indicates that the n-bit output value has converged (i.e., stopped changing) in the sending Ising device.

Now, with reference to FIGS. 2 and 3, the description turns to an extended ensemble method that the information processing apparatus 1 performs. This method may also be called an “exchange Monte Carlo method” or “ensemble exchange method.”

Here the term “ensemble” refers to a neural network with a particular temperature. The extended ensemble method exchanges states of nodes between different ensembles (i.e., different neural networks having different temperatures) during the course of a parallel probabilistic search performed in those ensembles. More specifically, exchanging of node states takes place between two ensembles having adjacent temperatures, depending on their energy difference. This method prevents the search from falling into a local optimal solution and thus makes it possible to reach the optimal value in a shorter time.

FIG. 2 illustrates how a plurality of ensembles with different temperatures exchange their node states. It is assumed in this example of FIG. 2 that four ensembles have been prepared and set up with successively increasing temperatures T₁, T₂, T₃, and T₄ (i.e., T₁<T₂<T₃<T₄). According to the extended ensemble method, two ensembles having adjacent temperatures exchange their node states with a certain exchange probability. Here the exchange probability may be expressed as min(1, R), where R is given by the following equation (1).

R=exp{(1/T _(q)−1/T _(q+1))(E _(total)(X _(q))−E _(total)(X _(q+1)))}  (1)

The symbols T_(q) and T_(q+1) in this equation (1) represent the temperatures of the q-th and (q+1)th ensembles. That is, temperatures T_(q) and T_(q+1) are adjacent to each other. E_(total)(X_(q)) and E_(total)(X_(q+1)) denote the total energies of the noted ensembles. X_(q) includes all the node states of the q-th ensemble, as does X_(q+1) for the (q+1)th ensemble.

As can be seen from equation (1), R exceeds one when T_(q)<T_(q+1) and E_(total)(X_(q))>E_(total)(X_(q+1)). This means that the exchange probability reaches one, thus causing an exchange of node states to happen. For example, an ensemble having a temperature of T₁ would exchange node states with an ensemble having a temperature of T₂ when the energy of the latter ensemble is smaller than the energy of the former ensemble.

In contrast, when T_(q)<T_(q+1) and E_(total)(X_(q))<E_(total)(X_(q+1)) an exchange of node states takes place with a probability of R. For example, an ensemble having a temperature of T₁ would exchange node states with an ensemble having a temperature of T₂ with a probability of R when the energy of the latter ensemble is larger than the energy of the former ensemble.

FIG. 3 illustrates energy functions of ensembles with different temperatures. Six curves (1) to (6) are seen in FIG. 3, representing energy functions of ensembles having successively decreasing temperatures. The topmost curve (1) is of the highest-temperature ensemble, and the bottommost curve (6) is of the lowest-temperature ensemble. As the temperature rises, the curve becomes gentler (i.e., has fewer peaks and bottoms, and the slopes are more gradual). For example, the topmost curve (1) is less likely to fall into a local optimal solution because it is gentler than the bottom most curve (6).

As described above, the extended ensemble method exchanges node states between two ensembles having adjacent temperatures. Suppose, for example, one ensemble has an energy function of curve (6). This ensemble may be trapped into a local optimal solution, but the noted exchanging of node states permits the ensemble to move to different node states that were previously of a higher-temperature ensemble. That is, the former ensemble may move to a different energy function of curve (5) with a certain exchange probability, thus exiting from the local optimal solution. This mechanism of the extended ensemble method permits faster convergence of solutions to an optimal point than the conventional simulated annealing methods. It is noted that the above-described extended ensemble method may be modified to exchange temperatures, instead of node states. The same advantages will be achieved also in this modified version.

In the proposed information processing apparatus of the first embodiment, the above-described extended ensemble method is implemented in the hardware circuitry. Specifically, the ensembles discussed above correspond to Ising devices 2 a 1 to 2 aN, and the node states correspond to the n-bit output value of each neuron circuit block 10 a 1 to 10 aN. The temperatures discussed above correspond to effective temperatures T₁ to T_(N) (or noise widths) given to the Ising devices 2 a 1 to 2 aN.

The calculation circuit 3 is configured to calculate energy values on the basis of local field values and n-bit output values. These energy values represent total energies of individual Ising devices 2 a 1 to 2 aN and are used as E_(total)(X_(q)) and E_(total)(X_(q+1)) in equation (6). Further, the exchange control circuit 4 is configured to exchange n-bit output values or noise widths between two of the Ising devices 2 a 1 to 2 aN that have adjacent noise widths, with an exchange probability min(1, R) based on the difference in energy values between the two Ising devices.

As can be seen from the above description, the proposed information processing apparatus 1 uses a hardware-based implementation of an extended ensemble method to obtain optimal solutions in a short time. The present embodiment thus reduces the time for solving optimization problems.

The calculation of exchange probabilities uses energy values. These energy values are obtained by performing MAC operations between local field values and output values at each neuron. The proposed calculation circuit 3 calculates energy values with a simple circuit structure for MAC operations.

(b) Second Embodiment

FIG. 4 illustrates an example of an information processing apparatus according to a second embodiment. Several elements in this information processing apparatus of FIG. 4 have the same reference numerals as their counterparts in FIG. 1.

The illustrated information processing apparatus 1 a includes Ising devices 2 b 1 to 2 bN, a controller device 5, and a random signal generator circuit 6. The Ising devices 2 b 1 to 2 bN in FIG. 4 are respectively set up with different effective temperatures T of T₁, T₂, . . . , and T_(N). Specifically, the Ising devices 2 b 1 to 2 bN in FIG. 4 are assumed to have successively smaller temperatures as in T₁>T₂> . . . >T_(N). As the Ising devices 2 b 1 to 2 bN have the same internal structure, the following description focuses on one Ising device 2 b 1 as a representative example.

The Ising device 2 b 1 includes a neuron circuit block 10 a 1, a control circuit 10 b 1, a calculation circuit 10 c 1, and an exchange control circuit 10 d 1. The Ising device 2 b 1 also includes a noise generator circuit 10 e 1 and a random signal generator circuit 10 f 1, which are omitted in FIG. 1. The calculation circuit 10 c 1 and exchange control circuit 10 d 1 provide the same functions as the calculation circuit 3 and exchange control circuit 4 in the foregoing first embodiment.

The neuron circuit block 10 a 1 includes n neuron circuits 1111 to 111 n. In the example of FIG. 4, the neuron circuits 1111 to 111 n are designed to execute processing based on what is called DeGloria algorithm.

(b1) Exemplary Neuron Circuit

FIG. 4 provides the details of two neuron circuits 1111 and 111 n, while omitting others because of their similarity to the neuron circuits 1111 and 111 n.

The first neuron circuit 1111 includes a register 20 a 1, selector circuits 21 a 1 and 22 a 1, a multiplier circuit 23 a 1, an adder circuit 24 a 1, another register 25 a 1, another adder circuit 26 a 1, a comparator circuit 27 a 1, an exclusive OR (XOR) gate 28 a 1, and yet another register 29 a 1. Similarly, the n-th neuron circuit 111 n includes a register 20 an, selector circuits 21 an and 22 an, a multiplier circuit 23 an, an adder circuit 24 an, another register 25 an, another adder circuit 26 an, a comparator circuit 27 an, an XOR gate 28 an, and yet another register 29 an.

The register 20 a 1 in the first neuron circuit 1111 stores therein n weight values W₁₂, W₁₃, . . . , and W_(1n). The register 20 an in the n-th neuron circuit 111 n stores therein n weight values W_(n1), W_(n2), . . . , and W_(nn). These weight values are specified by the controller device 5, depending on the problem to be solved, and entered to the registers 20 a 1 to 20 an. As an alternative, weight values may be stored in a random access memory (RAM) or other memory devices.

The selector circuit 21 a 1 in the first neuron circuit 1111 selects one of the weight values W₁₂ to W_(1n) stored in the register 20 a 1, based on a selection code signal from control circuit 10 b 1. Similarly, the selector circuit 21 an in the n-th neuron circuit 111 n selects one of the weight values W_(n1) to W_(nn) stored in the register 20 an, based on the same selection code signal. For example, when the first neuron circuit 1111 changes its output value, the selector circuit 21 an in the n-th neuron circuit 111 n selects a weight value W_(n1) according to a selection code signal.

When a neuron circuit changes its output value, the control circuit 10 b 1 outputs zero or one representing the changed output value. The selector circuits 22 a 1 to 22 an select either one (1) or minus one (−1) according to that output value supplied from the control circuit 10 b 1. When the output value is zero, the selector circuit 22 a 1 to 22 an selects one. When the output value is one, the selector circuit 22 a 1 to 22 an selects minus one. The reason for this operation will be described later.

The multiplier circuit 23 a 1 in the first neuron circuit 1111 calculates the product of outputs from the two selector circuits 21 a 1 and 22 a 1 described above. Similarly, the multiplier circuit 23 an in the n-th neuron circuit 111 n calculates the product of outputs from the two selector circuits 21 an and 22 an.

The adder circuit 24 a 1 in the first neuron circuit 1111 adds the output value of the multiplier circuit 23 a 1 to what the register 25 a 1 currently stores. Similarly, the adder circuit 24 an in the n-th neuron circuit 111 n adds the output value of the multiplier circuit 23 an to what the register 25 an currently stores.

The register 25 a 1 in the first neuron circuit 1111 takes in the output value of the adder circuit 24 a 1 in synchronization with a clock signal (not illustrated in FIG. 4). Similarly, the register 25 an in the n-th neuron circuit 111 n takes in the output value of the adder circuit 24 an in synchronization with a clock signal (not illustrated in FIG. 4). For example, the registers 25 a 1 to 25 an may be flip-flops. The registers 25 a 1 to 25 an are initialized with what will be described later as bias values.

The symbols h₁ and h_(n) seen inside the boxes representing registers 25 a 1 and 25 an in FIG. 4 are local field values. That is, the aforementioned local field values are stored in the registers 25 a 1 to 25 an.

The adder circuit 26 a 1 in the first neuron circuit 1111 adds a noise value to the output value of the register 25 a 1. The noise value is provided from the noise generator circuit 10 e 1. Similarly, the adder circuit 26 an in the n-th neuron circuit 111 n adds a noise value to the output value of the register 25 an. Some examples of noise values will be described later.

The noise generator circuit 10 e 1 outputs noise values under the control of the controller device 5. For example, the noise generator circuit 10 e 1 includes an amplifier circuit, and the controller device 5 varies the gain of this amplifier circuit so as to control the noise width corresponding to a given effective temperature.

The comparator circuit 27 a 1 in the first neuron circuit 1111 outputs a value of one if the output of the adder circuit 26 a 1 is greater than a threshold, and otherwise a value of zero. Similarly, the comparator circuit 27 an in the n-th neuron circuit 111 n outputs a value of one if the output of the adder circuit 26 an is greater than a threshold, and otherwise a value of zero.

Each comparator circuit 27 a 1 to 27 an has an enable input. These enable inputs of the comparator circuits 27 a 1 to 27 an are controlled individually, such that only one of the neuron circuits 1111 to 111 n in the Ising device 2 b 1 is allowed to change its output value at a time. More specifically, random values are generated by a random signal generator circuit 10 f 1 to enable a single randomly-selected comparator circuit while disabling the others. For example, the random signal generator circuit 10 f 1 may be implemented with a linear feedback shift register (LFSR). LFSR may also be used to implement the foregoing noise generator circuit 10 e 1.

The XOR gate 28 a 1 in the first neuron circuit 1111 outputs a value of zero when either the output of the comparator circuit 27 a 1 or a value supplied from the exchange control circuit 10 d 1 matches with the output of the register 29 a 1. Otherwise, the XOR gate 28 a 1 outputs a value of one. Similarly, the XOR gate 28 an in the n-th neuron circuit 111 n outputs a value of zero when either the output of the comparator circuit 27 an or a value supplied from the exchange control circuit 10 d 1 matches with the output of the register 29 an. Otherwise, the XOR gate 28 an outputs a value of one.

Although not explicitly illustrated in FIG. 4, each individual comparator circuit 27 a 1 to 27 an has its own selector circuit at its output end. This non-illustrated selector circuit is used to select one bit out of an n-bit output value X_(1new) supplied from the exchange control circuit 10 d 1 or the output value of its local comparator circuit 27 a 1 to 27 an. These n selector circuits as a whole select an n-bit output value X_(1new) when the exchange control circuit 10 d 1 outputs it. Instead of outputs of the comparator circuits 27 a 1 to 27 an, the individual bits of the selected n-bit output value X_(1new) are then supplied to the XOR gates 28 a 1 to 28 an and registers 29 a 1 to 29 an.

As noted above, the exchange control circuit 10 d 1 in the Ising device 2 b 1 supplies an n-bit output value X_(1new). This value is actually originated from the neuron circuit block 10 a 1 in the Ising device 2 b 1 itself or its counterpart (not illustrated in FIG. 4) in the next Ising device 2 b 2. For example, the first bit value of X_(1new) is supplied to the XOR gate 28 a 1 in the first neuron circuit 1111, and the n-th bit value of the same is supplied to the XOR gate 28 an in the n-th neuron circuit 111 n.

The register 29 a 1 in the first neuron circuit 1111 takes in a value from the comparator circuit 27 a 1 or from the exchange control circuit 10 d 1, when the XOR gate 28 a 1 outputs a value of one. This act means that the first neuron circuit 1111 changes (updates) its output value x₁. Similarly, the register 29 an in the n-th neuron circuit 111 n takes in a value from the comparator circuit 27 an or from the exchange control circuit 10 d 1, when the XOR gate 28 an outputs a value of one, thus changing the output value x_(n) of the n-th neuron circuit 111 n.

The above-described neuron circuits 1111 to 111 n implement an energy function E(x) in the Ising model with a relatively small hardware size. For example, the energy function E(x) is defined by the following equation (2).

$\begin{matrix} {{E(x)} = {{- {\sum\limits_{\langle{i,j}\rangle}\; {W_{ij}x_{i}x_{j}}}} - {\sum\limits_{i}{b_{i}x_{i}}}}} & (2) \end{matrix}$

The first term in the right-hand side is a sum of weighted products of two neuron circuit outputs x_(i) and x_(j), where weight values W_(ij)=W_(ji) and W_(ii)=0. The accumulation of products is performed with respect to every possible combination of two neuron circuits, with no missing or duplicated combinations.

The second term in the right-hand side is a sum of products between bias values and output values with respect to all the neuron circuits. The symbol b_(i) represents the bias value of the i-th neuron circuit.

For hardware-based implementation of the above energy function E(x), the neuron circuits 1111 to 111 n in FIG. 4 calculate their respective local field values h₁ to h_(n). For example, the following equation (3) gives a local field value h_(i) of the i-th neuron circuit 111 i, where 1≦i≦n.

$\begin{matrix} {h_{i} = {{\sum\limits_{j}{W_{ij}x_{j}}} + b_{i}}} & (3) \end{matrix}$

The first term in the right-hand side of equation (3) is a sum of products that represent weighted output values of the neuron circuits 1111 to 111 n. Here, each weight value W_(ij) denotes the strength of a connection between the i-th neuron circuit and another neuron circuit in the Ising device 2 b 1.

As mentioned above, the Ising device 2 b 1 is allowed to change only one output value at a time although it has many neuron circuits 1111 to 111 n. When such a change is made at a certain neuron circuit, other neuron circuits connected to that changing neuron circuit add the change to or subtract the change from their respective current local field values. Suppose, for example, that the j-th neuron circuit is coupled to input of the i-th neuron circuit, where 1≦j≦n. When the j-th neuron circuit changes its output value from x_(j) (0 or 1) to 1−x_(j), the local field value of the i-th neuron circuit makes a change Δh_(i) given by the following equation (4).

Δh _(i) =h _(i)|_(x) _(j) _(−1−x) _(j) −h _(i) =W _(ij)(1−2x _(j))  (4)

The difference (1−2x_(j)) seen in this equation (4) takes a value of −1 when the output value x₁ changes from 0 to 1, and a value of +1 when it changes from 1 to 0. This processing of (1−2x_(j)) is implemented in the selector circuits 22 a 1 to 22 an in FIG. 4.

As described previously, the neuron circuits 1111 to 111 n seen in FIG. 4 include comparator circuits 27 a 1 to 27 an to compare their respective local field values h₁ to h_(n) plus some noise value with a threshold. For example, noise values are determined such that the probability that the comparator circuits 27 a 1 to 27 an output a value of one (in other words, the output value x₁ to x_(n) of each neuron circuit 1111 to 111 n becomes one) will follow a sigmoid function. More specifically, a noise value is added to the local field value h_(i) so that the i-th neuron circuit will yield an output value x_(i)=1 with a probability P_(i)(h_(i)) seen below.

P _(i)(h _(i))=1/[1+exp(−h _(i) /T)]  (5)

The symbol T in equation (5) represents effective temperature. To achieve the above probability P_(i)(h_(i)) in equation (5), the noise values ns have to follow the probability density function of equation (6) below.

p(ns)=exp(−h _(i) /T)/[1+exp(−h _(i) /T)]²  (6)

FIG. 5 illustrates an exemplary distribution of probability P_(i)(h_(i)) that output value x_(i) takes a value of one. The horizontal axis represents the sum of local field value h_(i) and noise value ns, while the vertical axis represents the probability of x_(i)=1. FIG. 5 actually plots two graphs 30 and 31. The first graph 30 indicates the probability P_(i)(h_(i)) that the i-th neuron circuit yields an output value x_(i) of one when its comparator circuit receives a sum of local field value h_(i) and noise value ns, assuming that the noise value ns varies according to the foregoing probability density function p(ns) of equation (6). The second graph 31 indicates the probability P_(i)(h_(i)) that the i-th neuron circuit yields an output value x_(i) of one when its comparator circuit receives a local field value h_(i) alone.

Without noise values, the probability P_(i)(h_(i)) makes a stepwise change from zero to one, as seen in the second graph 31, at the point where the local field value h_(i) exceeds a threshold Vth. In contrast, with noise values ns added to the local field value h_(i), the probability P_(i)(h_(i)) moderately varies according to a sigmoid function as seen in the first graph 30.

This concludes the explanation of neuron circuits 1111 to 111 n.

(b2) Calculation Circuit

FIG. 6 illustrates an example of a calculation circuit. This calculation circuit 10 c 1 includes a multiplier circuit 40, an adder circuit 41, and a register 42. These components work as follows.

The multiplier circuit 40 calculates a product of an output value x_(i) and a local field value h_(i). The output value x_(i) refers to the i-th bit of an n-bit output value X₁ from the neuron circuit block 10 a 1. The local field value h_(i) is a value stored in a register in the i-th neuron circuit 111 i, where 1≦i≦n. The adder circuit 41 calculates a sum of the current value in the register 42 and the above product calculated by the multiplier circuit 40. The register 42 takes in this sum from the adder circuit 41 in synchronization with a clock signal (not illustrated in FIG. 6).

The calculation circuit 10 c 1 receives each output value x_(i) and each local field value h_(i), where i is an integer number that varies in the range of one to n. With the circuit structure of FIG. 6, the calculation circuit 10 c 1 performs MAC operations between output values x₁ to x_(n) and local field values h₁ to h_(n). The result of the MAC operations is referred to as an energy value E_(total)(X₁). This energy value E_(total)(X₁) represents the total amount of energy in the Ising device 2 a 1.

(b3) Exchange Control Circuit

As part of the circuits designed for the foregoing extended ensemble method, the exchange control circuit 10 d 1 in FIG. 4 exchanges n-bit output values between two Ising devices 2 a 1 and 2 a 2 with an exchange probability based on a difference between the two Ising devices in terms of the energy values discussed above.

FIG. 7 illustrates an example of an exchange control circuit. This exchange control circuit 10 dq of FIG. 7 represents N exchange control circuits 10 d 1 to 10 dN in the Ising devices 2 b 1 to 2 bN. Specifically, the exchange control circuit 10 dq is the one in the q-th Ising device 2 bq, where 1≦q≦N. The exchange control circuit 10 dq is formed from first and second flag generator circuits 50 and 51, an AND gate 52, and an exchange circuit 53.

The first flag generator circuit 50 receives an energy value E_(total)(X_(q)) representing the total amount of energy in the q-th Ising device itself. The first flag generator circuit 50 also receives an energy value E_(total)(X_(q+1)) representing the total amount of energy in the (q+1)th Ising device. The (q+1)th Ising device has an effective temperature T_(q+1) higher than the q-th Ising device's T_(q). The first flag generator circuit 50 further receives a random value from the random signal generator circuit 6. Based on the received two energy values E_(total)(X_(q)) and E_(total)(X_(q+1)) and random value, the first flag generator circuit 50 generates and outputs a flag signal Flgd. This flag signal Flgd indicates whether to cause the neuron circuits in the q-th and (q+1)th Ising devices to exchange their n-bit output values X_(q) and X_(q+1). When flag signal Flgd is asserted to one, it means that output values X_(q) and X_(q+1) are to be exchanged with each other. When flag signal Flgd stays zero, it means that no exchange is to be made between two output values X_(q) and X_(q+1).

The second flag generator circuit 51 receives an energy value E_(total)(X_(q)) representing the total amount of energy in the q-th Ising device. The second flag generator circuit 51 also receives an energy value E_(total)(X_(q−1)) representing the total amount of energy in the (q−1)th Ising device. The (q−1)th Ising device has an effective temperature T_(q−1) lower than the q-th Ising device's T_(q). The second flag generator circuit 51 further receives a random value from the random signal generator circuit 6. Based on the received two energy values E_(total)(X_(q)) and E_(total)(X_(q−1)) and random value, the second flag generator circuit 51 generates and outputs a flag signal Flgu. This flag signal Flgu indicates whether to cause the neuron circuits in the q−th and (q−1)th Ising devices to exchange their n-bit output values X_(q) and X_(q−1). When flag signal Flgu is asserted to one, it means that output values X_(q) and X_(q−1) are to be exchanged with each other. When flag signal Flgu stays zero, it means that no exchange is to be made between output values X_(q) and X_(q−1).

FIG. 8 illustrates an example of a flag generator circuit. More particularly, FIG. 8 illustrates an example of the first flag generator circuit 50. The first flag generator circuit 50 may be designed to operate on the basis of what is called the Metropolis-Hastings algorithm. The illustrated first flag generator circuit 50 is formed from an energy comparator circuit 60, a probability computation circuit 61, a probability comparator circuit 62, and an OR gate 63.

The energy comparator circuit 60 compares energy values E_(total)(X_(q)) and E_(total)(X_(q+1)). When E_(total)(X_(q)) is greater than E_(total)(X_(q+1)), the energy comparator circuit 60 outputs a value of one. When E_(total)(X_(q)) is smaller than E_(total)(X_(q+1)), the energy comparator circuit 60 outputs a value of zero.

The probability computation circuit 61 calculates a probability R according to equation (1). Specifically, the probability computation circuit 61 is formed from a subtracter circuit 61 a, a multiplier circuit 61 b, and an exponential operator circuit 61 c. The subtracter circuit 61 a calculates a difference between two energy values E_(total)(X_(q)) and E_(total)(X_(q−1)). The multiplier circuit 61 b outputs a product of the difference and a constant K stored in a register (not illustrated). The constant K has a value of (1/T_(q))−(1/T_(q+1)), which is calculated by the controller device 5, for example. The exponential operator circuit 61 c then calculates a probability R of equation (1) from the output of the multiplier circuit 61 b by using a natural exponential function.

The probability comparator circuit 62 compares the above probability R with a random value provided from the random signal generator circuit 6. Here the random value is assumed to be greater than zero and smaller than one. When the random number is greater than probability R, the probability comparator circuit 62 outputs a value of one. When the random number is smaller than probability R, the probability comparator circuit 62 outputs a value of zero.

The OR gate 63 performs a logical disjunction of two output values from the energy comparator circuit 60 and probability comparator circuit 62. The result of this operation is a flag signal Flgd.

The second flag generator circuit 51 is similar to the first flag generator circuit 50 described above. Specifically, the second flag generator circuit 51 may be implemented by modifying the first flag generator circuit of FIG. 8 as follows: (a) energy value E_(total)(X_(q−1)) is used in place of energy value E_(total)(X_(q)), (b) energy value E_(total)(X_(q)) is used in place of energy value E_(total)(X_(q+1)), and (c) the flag signal output is not Flgd, but Flgu.

FIG. 9 illustrates another example of a flag generator circuit. Specifically, FIG. 9 illustrates a first flag generator circuit 50 a designed to operate according to what is called Heat-Bath algorithm, as an alternative implementation of the first flag generator circuit 50 discussed in FIG. 7. The illustrated circuit structure of the first flag generator circuit 50 a may similarly be used to implement the second flag generator circuit 51 in FIG. 7.

The first flag generator circuit 50 a is formed from a probability computation circuit 71 and a probability comparator circuit 72. The probability computation circuit 71 calculates a probability R according to equation (7) below. To this end, the probability computation circuit 71 includes a subtracter circuit 71 a, a multiplier circuit 71 b, an exponential operator circuit 71 c, an adder circuit 71 d, and a divider circuit 71 e.

R=1/[1+exp{(1/T _(q)−1/T _(q+1))(E _(total)(X _(q+1))−E _(total)(X _(q)))}]  (7)

The subtracter circuit 71 a, multiplier circuit 71 b, and exponential operator circuit 71 c perform the same computational operations discussed above for the subtracter circuit 61 a, multiplier circuit 61 b, and exponential operator circuit 61 c in FIG. 8. The adder circuit 71 d adds one to the result value of the exponential operator circuit 61 c. The divider circuit 71 e then calculates a reciprocal of the summation result of the adder circuit 71 d, thus yielding a probability R of equation (7).

The probability comparator circuit 72 compares the above probability R with a random value from the random signal generator circuit 6. Here the random value is assumed to be greater than zero and smaller than one. When the random number is greater than probability R, the probability comparator circuit 72 outputs a value of one as flag signal Flgd. When the random number is smaller than probability R, the probability comparator circuit 72 outputs a value of zero as flag signal Flgd.

Referring back to FIG. 7, the AND gate 52 performs a logical product operation on two flag signals Flgd and Flgu generated by the first and second flag generator circuits 50 and 51. The result of this operation is referred to as an arbitration signal Arbi. That is, the AND gate 52 asserts the arbitration signal Arbi to one when both flag signals Flgd and Flgu are one. Otherwise, the arbitration signal Arbi is zero.

The exchange circuit 53 receives the flag signals Flgd and Flgu from the first and second flag generator circuits 50 and 51 and the arbitration signal Arbi from the AND gate 52. The exchange circuit 53 also receives n-bit output values X_(q−1), X_(q), and X_(q+1) from neuron circuits in the (q−1)th, q-th, and (q+1)th Ising devices, respectively. Based on these signals, the exchange circuit 53 generates a new n-bit output value X_(qnew) for use in neuron circuits of the q-th Ising device.

FIG. 10 illustrates an example of an exchange circuit. The illustrated exchange circuit 53 includes a selection signal generator circuit 80 and a state selection circuit 81. The selection signal generator circuit 80 outputs two selection signals Selu and Seld according to a truth table seen in FIG. 11, based on the flag signals Flgd and Flgu and the arbitration signal Arbi from the AND gate 52.

FIG. 11 illustrates a truth table that indicates an exemplary relationship between input signals and output signals of a selection signal generator circuit. As the truth table of FIG. 11 indicates, the selection signal generator circuit 80 outputs selection signals Selu=1 and Seld=0 when flag signal Flgu is one while flag signal Flgd and arbitration signal Arbi are zero. The selection signal generator circuit 80 outputs selection signals Selu=0 and Seld=1 when flag signal Flgd is one while flag signal Flgu and arbitration signal Arbi are zero. The selection signal generator circuit 80 outputs selection signals Selu=0 and Seld=0 when flag signals Flgu and Flgd and arbitration signal Arbi are zero. The selection signal generator circuit 80 outputs selection signals Selu=1 and Seld=0 (or Selu=0 and Seld=1) when flag signals Flgu and Flgd and arbitration signal Arbi are one.

Referring back to FIG. 10, the state selection circuit 81 generates a new n-bit output value X_(qnew) for use in neuron circuits of the q-th Ising device, based on selection signals Selu and Seld from the selection signal generator circuit 80. As will be described below, the state selection circuit 81 follows a truth table in FIG. 12.

FIG. 12 illustrates a truth table that indicates an exemplary relationship between input signals and output signals of a state selection circuit. As the truth table of FIG. 12 indicates, the state selection circuit 81 selects output value X_(q−1) of the (q−1)th Ising device and outputs it as a new output value X_(qnew) when selection signal Selu is one while selection signal Seld is zero. When this is the case, the q-th and (q−1)th Ising devices exchange their output values X_(q) and X_(q−1).

The state selection circuit 81 selects output value X_(q−1) of the (q+1)th Ising device and outputs it as a new output value X_(qnew) when selection signal Selu is zero while selection signal Seld is one. When this is the case, the q-th and (q+1)th Ising devices exchange their output values X_(q) and X_(q+1).

The state selection circuit 81 selects output value X_(q) of the q-th Ising device and outputs it as an output value X_(qnew) when both selection signals Selu and Seld are zero. When this is the case, no exchange of output values takes place among the (q−1)th, q-th, and (q+1)th Ising devices.

(b4) Exemplary Operation of Information Processing Apparatus According to Second Embodiment

With reference to several flowcharts, this subsection describes how the information processing apparatus 1 a of FIG. 4 operates under the control of the controller device 5.

FIGS. 13 and 14 are a flowchart illustrating exemplary operation of the information processing apparatus 1 a according to the second embodiment.

(Step S1) Upon receipt of a startup signal from an external source, the controller device 5 configures Ising devices 2 b 1 to 2 bN with different effective temperatures (noise widths).

(Step S2) In each Ising device 2 b 1 to 2 bN, its n neuron circuits (e.g., neuron circuits 1111 to 111 n) calculate their respective local field values h₁ to h_(n).

(Step S3) In each Ising device 2 b 1 to 2 bN, its n neuron circuits add noise values to their respective local field values h₁ to h_(n).

(Step S4) Each Ising device 2 b 1 to 2 bN allows one of its n neuron circuits to update its output value. This selection of one neuron circuit depends on a random value supplied from a random signal generator circuit included in each Ising device 2 b 1 to 2 bN (e.g., random signal generator circuit 10 f 1). The control circuit in each Ising device 2 b 1 to 2 bN (e.g., control circuit 10 b 1) then increments a selection counter by one to record the selection.

(Step S5) In each Ising device 2 b 1 to 2 bN, the selected neuron circuit determines whether the sum of its own local field value and a noise value exceeds a threshold. When the sum exceeds the threshold, the process advances to step S6. Otherwise, the process skips to step S7.

(Step S6) In each Ising device 2 b 1 to 2 bN, its control circuit (e.g., control circuit 10 b 1) supplies the n neuron circuits with the updated output value of the selected neuron circuit, as well as with a selection signal for a weight value associated with the selected neuron circuit.

(Step S7) In each Ising device 2 b 1 to 2 bN, its control circuit (e.g., control circuit 10 b 1) determines whether the selection counter has reached a specified limit. When the specified limit is reached, the process advances to step S8. Otherwise, the process goes back to step S2 to repeat the above steps.

(Step S8) In each Ising device 2 b 1 to 2 bN, its calculation circuit (e.g., calculation circuit 10 c 1) obtains local field values h₁ to h_(n) and output values from the n neuron circuits. The calculation circuits in the Ising devices 2 b 1 to 2 bN calculate their respective energy values E_(total)(X₁) to E_(total)(X_(N)). The energy values E_(total)(X₁) to E_(total)(X_(N)) represent the total amount of energy in the individual Ising devices 2 b 1 to 2 bN.

(Step S9) The exchange control circuits 10 d 1 to 10 dN determine whether to exchange output values. For example, one exchange control circuit 10 d 1 obtains an energy value E_(total)(X₁) from the calculation circuit 10 c 1 and an n-bit output value X₁ from the control circuit 10 b 1. The exchange control circuit 10 d 1 also obtains an energy value E_(total)(X₂) and an n-bit output value X₂ from its counterpart exchange control circuit 10 d 2 in the adjacent Ising device 2 b 2. The energy value E_(total)(X₂) represents the total amount of energy in the Ising device 2 b 2. The exchange control circuit 10 d 1 now calculates an exchange probability on the basis of a difference between the two energy values E_(total)(X₁) and E_(total)(X₂). Then based on this exchange probability, the exchange control circuit 10 d 1 determines whether to exchange the output values X₁ and X₂ with each other.

(Step S10) When any two of the exchange control circuits 10 d 1 to 10 dN are to exchange their output values X₁ to X_(N), they advance to step S11, and otherwise skip to step S12.

(Step S11) Since the above step S9 has determined two adjacent Ising devices to exchange output values, the exchange control circuits 10 d 1 to 10 dN in those adjacent Ising devices exchange their n-bit output values (i.e., the outputs of their neuron circuit blocks) with each other.

Suppose, for example, that two Ising devices 2 b 1 and 2 b 2 are about to exchange their output values. In this case, their exchange control circuits 10 d 1 and 10 d 2 exchange n-bit outputs X₁ and X₂ of their neuron circuit blocks 10 a 1 and 10 a 2 (the latter is not illustrated in FIG. 4). Accordingly, the exchange control circuit 10 d 1 supplies X₂ to its local neuron circuits 1111 to 111 n as a new output value X_(1new) for them.

(Step S12) The control circuit in each Ising device 2 b 1 to 2 bN (e.g., control circuit 10 b 1) obtains the n-bit output value from its local neuron circuit block.

(Step S13) Each control circuit determines whether the n-bit output value obtained in step S12 has any change. When there is no change in the n-bit output value, the process advances to step S14. Here the corresponding control circuit increments its no-change counter by one, the counter indicating how many cycles the n-bit output value stays unchanged. When the n-bit output value has a change, the process returns to step S2 to repeat the above steps.

(Step S14) Each control circuit determines whether its no-change counter for n-bit output values has reached a specified limit. When the specified limit is reached, the corresponding control circuit notifies the controller device 5 that the computation in its Ising device has converged. In response, the controller device 5 generates a signal that indicates completion of the computation. When the specified limit is not reached, the process returns to step S2 to repeat the above steps.

The structure and operation of an information processing apparatus 1 a according to the second embodiment has been described above. The information processing apparatus 1 a exchanges n-bit output values of Ising devices having adjacent noise widths (or effective temperatures). This exchange happens with an exchange probability of (1, R), under the control of exchange control circuits 10 d 1 to 10 dN. The second embodiment provides a hardware-based implementation of the foregoing extended ensemble method, making it possible to reach an optimal solution of a problem in a shorter time. That is, the second embodiment reduces the processing time for solving optimization problems.

The exchange probability is calculated from energy values of neuron circuits, and the energy values are calculated by repeating multiply-accumulate operations of local field values and output values in the individual neuron circuits. It is thus possible to calculate, for example, an energy value E_(total)(X₁) with a simple calculation circuit 10 c 1 discussed in FIG. 6.

(c) Third Embodiment

FIG. 15 illustrates an example of an information processing apparatus according to a third embodiment. Several elements in this information processing apparatus of FIG. 15 have the same reference numerals as their counterparts in the information processing apparatus 1 a of FIG. 4.

The illustrated information processing apparatus 1 b includes Ising devices 2 c 1 to 2 cN, a controller device 5, and an exchange control circuit 7. The Ising devices 2 c 1 to 2 cN in FIG. 15 are respectively set up with different effective temperatures T of T₁, T₂, . . . , and T_(N). Specifically, the Ising devices 2 b 1 to 2 bN in FIG. 4 are assumed to have successively smaller temperatures as in T₁>T₂> . . . >T_(N). Since the Ising devices 2 c 1 to 2 cN have the same circuit structure, the following description focuses on one Ising device 2 c 1 as a representative example.

The Ising device 2 c 1 has a neuron circuit block 10 a 1, a control circuit 10 b 1, and a calculation circuit 10 c 1 similarly to the foregoing Ising device 2 b 1 in FIG. 4. The Ising device 2 c 1, however, lacks the exchange control circuit 10 d 1 discussed in FIG. 4. Instead, a single exchange control circuit 7 is shared by the Ising devices 2 c 1 to 2 cN in this example of FIG. 15. It is not intended, however, to limit the third embodiment to the illustrated configuration. The functions of the exchange control circuit 7 may be implemented wholly or partly in the individual Ising devices 2 c 1 to 2 cN.

(c1) Exchange Control Circuit

The exchange control circuit 7 controls the process of exchanging noise widths between two of the Ising devices 2 c 1 to 2 cN, where the two Ising devices are set up with adjacent noise widths (or adjacent effective temperatures). An exchange of noise widths happens with a probability based on a difference in the foregoing energy values between the two Ising devices. Such exchanging of noise widths is part of the extended ensemble method described previously.

FIG. 16 illustrates an example of an exchange control circuit. This exchange control circuit 7 of FIG. 16 is formed from a random signal generator circuit 90, flag generator circuits 91 a 1, 91 a 2, . . . , 91 aq, 91 a(q+1), . . . , and 91 a(N−1), and a temperature setting signal generator circuit 92.

The random signal generator circuit 90 generates random values in the range from zero to one, as in the foregoing random signal generator circuit 6 of the second embodiment.

The flag generator circuits 91 a 1 to 91 a(N−1) in FIG. 16 may be implemented with the same circuit configuration discussed in FIGS. 8 and 9 for the first flag generator circuits 50 and 50 a in the second embodiment. For example, the q-th flag generator circuit 91 aq receives an energy value E_(total)(X_(q)) representing the total amount of energy in the q-th Ising device, as well as an energy value E_(total)(X_(q+1)) representing the total amount of energy in the (q+1)th Ising device. The q-th flag generator circuit 91 aq also receives a random value from the random signal generator circuit 90. Based on the received two energy values E_(total)(X_(q)) and E_(total)(X_(q+1)) and random value, the q-th flag generator circuit 91 aq generates and outputs a flag signal Flgq. This flag signal Flgq indicates whether to cause the q-th and (q+1)th Ising devices to exchange their noise widths (effective temperatures). Specifically, when flag signal Flgq is one, it means that the two Ising devices are to exchange their noise widths with each other. When flag signal Flgq is zero, it means that no such exchange is to be made.

The (q+1)th flag generator circuit 91 a(q+1) receives an energy value E_(total)(X_(q+1)) representing the total amount of energy in the (q+1)th Ising device, as well as an energy value E_(total)(X_(q+2)) representing the total amount of energy in the (q+2)th Ising device. The (q+1)th flag generator circuit 91 aq also receives a random value from the random signal generator circuit 90. Based on the received two energy values E_(total)(X_(q+1)) and E_(total)(X_(q+2)) and random value, the (q+1)th flag generator circuit 91 a(q+1) generates and outputs a flag signal Flg(q+1). This flag signal Flg(q+1) indicates whether to cause the (q+1)th and (q+2)th Ising devices to exchange their noise widths. Specifically, when flag signal Flg(q+1) is one, it means that the two Ising devices are to exchange their noise widths with each other. When flag signal Flg(q+1) is zero, it means that no such exchange is to be made.

The temperature setting signal generator circuit 92 generates temperature setting signals T_(S1), T_(S2), . . . , T_(Sq), T_(sq+1), . . . , and T_(SN) for setting noise widths corresponding to effective temperatures. As mentioned earlier, the noise generator circuit included in each Ising device 2 c 1 to 2 cN (e.g., noise generator circuit 10 e 1) has an amplifier circuit (not illustrated in FIG. 15). A temperature setting signal controls the gain of this amplifier, thereby setting an intended noise width to the corresponding Ising device. For example, temperature setting signal T_(S1) gives a specific noise width to the first Ising device 2 c 1, and temperature setting signal T_(S2) gives a specific noise width to the second Ising device 2 c 2.

In operation, the temperature setting signal generator circuit 92 first initializes the noise width of each noise generator circuit in the Ising devices 2 c 1 to 2 cN by controlling temperature setting signals T_(S1) to T_(SN) upon receipt of a startup signal from the controller device 5. These initial noise widths have been specified by the controller device 5, and the temperature setting signal generator circuit 92 holds them in its internal storage. Afterwards, the temperature setting signal generator circuit 92 may exchange noise widths between two of the Ising devices 2 c 1 to 2 cN, based on flag signals Flg1 to Flg(N−1) provided from the flag generator circuits 91 a 1 to 91 a(N−1). Here the two Ising devices are adjacent in terms of the values of noise width.

FIG. 17 illustrates an example of a temperature setting signal generator circuit. This temperature setting signal generator circuit 92 of FIG. 17 includes, among others, a selection signal generator circuit 100, an initializing circuit 101, a one-shot pulse generator circuit 102, and selector circuits 103 a 1, 103 a 2, . . . , 103 aq, 103 a(q+1), . . . , and 103 aN. The temperature setting signal generator circuit 92 further includes registers 104 a 1, 104 a 2, . . . , 104 aq, 104 a(q+1), . . . , and 104 aN, and a temperature switching circuit 105.

The selection signal generator circuit 100 outputs selection signals Sel1 to Sel(N−1) according to a truth table seen in FIG. 18, based on flag signals Flg1 to Flg(N−1). FIG. 18 illustrates a truth table that indicates an exemplary relationship between input signals and output signals of a temperature setting signal generator circuit. The symbol “d” in this truth table denotes “don't care” (i.e., its value, zero or one, does not matter).

As seen from the truth table of FIG. 18, the selection signal generator circuit 100 outputs selection signals Sel1=0 to SelN=0 when all input flag signals Flg1 to Flg(N−1) are zero. When flag signal Flg1 is one, the selection signal generator circuit 100 asserts its corresponding selection signal Sel1 to one while making all the other selection signals zero, no matter what values the other flag signals Flg2 to Flg(N−1) may take. When the (q+1)th flag signal Flg(q+1) is one whereas flag signals Flg1 to Flgq are zero, the selection signal generator circuit 100 asserts the (q+1)th selection signal Sel(q+1) to one while making all the other selection signals zero, regardless of the other flag signals.

The initializing circuit 101 holds a plurality of different initial values of noise widths (effective temperatures) for use in the individual Ising devices 2 b 1 to 2 bN. As mentioned above, these initial values are specified by the controller device 5, and the initializing circuit 101 receives and stores them. The initializing circuit 101 provides its stored values for setting initial values of temperature setting signals.

The one-shot pulse generator circuit 102 generates a one-shot pulse signal to selector circuits 103 a 1 to 103 aN in response to a startup signal from the controller device 5.

The selector circuits 103 a 1 to 103 aN select the aforementioned initial values of temperature setting signals from the initializing circuit 101 during the period of the one-shot pulse signal (e.g., when the one-shot pulse signal is at a logical high level). When there is no pulse signal (e.g., when the one-shot pulse signal is at a logical low level), the selector circuits 103 a 1 to 103 aN select the current values of temperature setting signals T_(S1) to T_(SN) of the temperature switching circuit 105.

The registers 104 a 1 to 104 aN receive and store temperature setting signals supplied from their corresponding selector circuits 103 a 1 to 103 aN.

The temperature switching circuit 105 outputs temperature setting signal T_(S1) to T_(SN), based on the foregoing selection signals Sel1 to Sel(N−1) from the selection signal generator circuit 100. Suppose, for example, that flag signals Flg1 to Flg(N−1) are zero when the one-shot pulse signal is at a logical high level. Because every selection signal Sel1 to Sel(N−1) is zero at this point in time, the temperature switching circuit 105 outputs temperature setting signals T_(S1) to T_(SN) carrying initial values for the Ising devices 2 c 1 to 2 cN. Accordingly, the Ising devices 2 c 1, 2 c 2, . . . , and 2 cN are respectively set up with their initial effective temperatures T of T₁, T₂, . . . , and T_(N).

The one-shot pulse signal then returns to a logical low level. The selection signals Sel1 to Sel(N−1) may be asserted to one in accordance with the truth table of FIG. 18 during the course of neural computation. When one selection signal is asserted, the temperature switching circuit 105 exchanges noise widths of the corresponding Ising devices 2 c 1 to 2 cN. Suppose, for example, that the q-th selection signal Selq is asserted to one. Then the temperature switching circuit 105 routes the value of temperature setting signal T_(Sq) from the q-th register 104 aq to the output of temperature setting signal T_(Sq+1), so that the (q+1)th Ising device will be set up with a noise width corresponding to T_(Sq). The temperature switching circuit 105 also routes the value of temperature setting signal T_(Sq+1) from the (q+1)th register 104 a (q+1) to the output of temperature setting signal T_(Sq), so that the q-th Ising device will be set up with a noise width corresponding to T_(Sq+1). This switching action in the temperature switching circuit 105 causes the q-th and (q+1)th Ising devices to exchange their noise widths with each other.

(c2) Exemplary Operation of Information Processing Apparatus According to Third Embodiment

With reference to a flowchart of FIG. 19, this subsection describes how the information processing apparatus 1 b of FIG. 15 operates under the control of the controller device 5.

FIG. 19 is a flowchart illustrating exemplary operation of an information processing apparatus according to the third embodiment. The proposed information processing apparatus 1 b executes steps S1 to S8 discussed in FIGS. 13 and 14 in the same way as the foregoing information processing apparatus 1 a does in the second embodiment. For these steps S1 to S8, see the preceding description of FIGS. 13 and 14. The following description thus begins with step S9 a in FIG. 19.

(Step S9 a) The exchange control circuit 7 determines whether to exchange noise widths. Specifically, the exchange control circuit 7 receives energy values E_(total)(X₁) to E_(total)(X_(N)) from Ising devices 2 c 1 to 2 cN and calculates a difference in energy value between each two adjacent Ising devices. Then based on exchange probabilities calculated from the differences, the exchange control circuit 7 determines whether to exchange noise widths between any two adjacent Ising devices and which two of the Ising devices 2 c 1 to 2 cN they are.

(Step S10 a) When it has determined to exchange noise widths, the exchange control circuit 7 advances to step S11 a, and otherwise skips to step S12.

(Step S11 a) The exchange control circuit 7 exchanges noise widths between the two adjacent Ising devices that have been determined in step S9 a.

The information processing apparatus 1 b executes the rest of the process, steps S12 to S14, similarly to the second embodiment.

FIG. 20 is a timing diagram illustrating exemplary operation of the information processing apparatus. Upon power-up of the information processing apparatus 1 b (time t1), the controller device 5 is brought to an initial state by a reset signal. The reset signal is then negated (time t2). This allows the controller device 5 to initialize parameters (e.g., weight values and bias values) as well as effective temperatures or noise widths (time t3 to time t4). Then the controller device 5 sends the exchange control circuit 7 a startup signal (time t5). As the startup signal is asserted to a logical high level, the foregoing steps S2 to S14 are executed.

The controller device 5 receives a neuron settlement signal from one of the Ising devices 2 c 1 to 2 cN (time t6). This neuron settlement signal indicates that the n-bit output value of the sending Ising device has settled, meaning that the problem has converged into a solution. In response, the controller device 5 outputs an end signal to indicate the completion of computation while negating the startup signal to a logical low level (time t7).

The above operation discussed in FIG. 20 is also valid for the second embodiment. In other words, the foregoing information processing apparatus 1 a may also operate almost similarly.

The structure and operation of an information processing apparatus 1 b according to the third embodiment has been described above. The information processing apparatus 1 b has an exchange control circuit 7 to exchange noise widths (effective temperatures) between two adjacent Ising devices, with an exchange probability of (1, R). The third embodiment provides a hardware-based implementation of an extended ensemble method, making it possible to reach an optimal solution of a problem in a shorter time. That is, the third embodiment reduces the processing time for solving optimization problems.

The information processing apparatus 1 b of the third embodiment exchanges noise widths, whereas the information processing apparatus 1 a of the second embodiment exchange n-bit output values generated by n neuron circuits. This means that the third embodiment reduces the amount of data to be exchanged.

The above embodiments have demonstrated one aspect of features that are provided by the proposed information processing apparatuses, Ising devices, and control method for controlling an information processing apparatus. It is noted, however, that what have been described above are only for illustrative purposes. It not intended to limit the scope by the described examples. For instance, the foregoing neuron circuit block is not limited to the one based on the DeGloria algorithm illustrated in FIG. 4 or other drawings. Rather, a neuron circuit block may be implemented in a different way, as long as it calculates local field values (i.e., energy of neurons) from n-bit output values from n neurons and their corresponding weight values.

Several examples of an information processing apparatus, an Ising device, and a control method have been discussed above. In one aspect, the proposed techniques contribute to reduction of computation time.

All examples and conditional language provided herein are intended for the pedagogical purposes of aiding the reader in understanding the invention and the concepts contributed by the inventor to further the art, and are not to be construed as limitations to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although one or more embodiments of the present invention have been described in detail, it should be understood that various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention. 

What is claimed is:
 1. An information processing apparatus comprising: a plurality of Ising devices each including a neuron circuit block that calculates as many first energy values as a number of neurons, based on weight values representing strengths of neuron-to-neuron connections and output values of the neurons, and determines and outputs new output values, based on comparison results between a threshold and each of the first energy values plus a noise value, the plurality of Ising devices having equal conditions about neuron-to-neuron connections represented by the weight values, the plurality of Ising devices being set up with different noise widths each representing a difference between a lower limit and an upper limit of noise values; a calculation circuit that calculates second energy values respectively representing total energies of the plurality of Ising devices, based on the first energy values and the output values; an exchange control circuit that exchanges output values or noise widths between a first Ising device and a second Ising device among the plurality of Ising devices, with an exchange probability based on a difference in the second energy values between the first Ising device and the second Ising device, the first and second Ising devices respectively having first and second noise widths, the second noise width being adjacent to the first noise width; and a controller device that sets the different noise widths to the plurality of Ising devices.
 2. The information processing apparatus according to claim 1, wherein the calculation circuit performs multiply-accumulate operations between the first energy values and the output values and outputs a result of the multiply-accumulate operations as one of the second energy values.
 3. The information processing apparatus according to claim 1, wherein: the second noise width is larger than the first noise width; and the exchange control circuit exchanges the output values or noise widths between the first Ising device and the second Ising device when the second Ising device has a smaller second energy value than the first Ising device.
 4. The information processing apparatus according to claim 3, wherein the exchange control circuit exchanges the output values or noise widths between the first Ising device and the second Ising device, when the second Ising device has a larger second energy value than the first Ising device, and when the exchange probability is smaller than a random value between zero and one.
 5. An Ising device comprising: a neuron circuit block that calculates as many first energy values as a number of neurons, based on weight values representing strengths of neuron-to-neuron connections and output values of the neurons, and determines and outputs new output values, based on comparison results between a threshold and each of the first energy values plus a noise value assigned to the Ising device, the noise value being variable within a first noise width that represents a difference between a lower limit and an upper limit of the noise value; a calculation circuit that calculates a second energy value representing a total energy of the Ising device, based on the first energy values and the output values; and an exchange control circuit that receives a third energy value representing a total energy of another Ising device having a second noise width adjacent to the first noise width and exchanges output values or noise widths between the Ising device and the another Ising device, with an exchange probability based on a difference between the second energy value and the third energy value, the second noise width representing a difference between a lower limit and an upper limit of a noise value used in the another Ising device.
 6. A method for controlling an information processing apparatus, the method comprising: setting, by a controller device in the information processing apparatus, different noise widths respectively to a plurality of Ising devices in the information processing apparatus, the noise widths each representing a difference between a lower limit and an upper limit of noise values, the plurality of Ising devices each including a neuron circuit block that calculates as many first energy values as a number of neurons, based on weight values representing strengths of neuron-to-neuron connections and output values of the neurons, and determines and outputs new output values, based on comparison results between a threshold and each of the first energy values plus a noise value, the plurality of Ising devices having equal conditions about neuron-to-neuron connections represented by the weight values; calculating, by a calculation circuit in the information processing apparatus, second energy values respectively representing total energies of the plurality of Ising devices, based on the first energy values and the output values; and exchanging, by an exchange control circuit in the information processing apparatus, output values or noise widths between a first Ising device and a second Ising device among the plurality of Ising devices, with an exchange probability based on a difference in the second energy values between the first Ising device and the second Ising device, the first and second Ising devices respectively having first and second noise widths, the second noise width being adjacent to the first noise width. 